A unified framework for interpolating and approximating univariate subdivision

DOI10.1016/j.amc.2010.02.009zbMath1195.65016OpenAlexW2084930303MaRDI QIDQ972164

Lucia Romani, Carolina Vittoria Beccari, Giulio Casciola

Publication date: 25 May 2010

Published in: Applied Mathematics and Computation (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.amc.2010.02.009

zbMATH Keywords

interpolationapproximationgenerating functionlink polynomial factorizationsubdivision surface refinementuniform univariate subdivision

Mathematics Subject Classification ID

Numerical aspects of computer graphics, image analysis, and computational geometry (65D18)

Related Items (18)

Exponential pseudo-splines: looking beyond exponential B-splines ⋮ Totally positive refinable functions with general dilation \(M\) ⋮ Non-uniform Doo-Sabin subdivision surface via eigen polygon ⋮ Construction of a family of non-stationary combined ternary subdivision schemes reproducing exponential polynomials ⋮ Non-uniform interpolatory subdivision surface ⋮ On interpolatory subdivision from approximating subdivision scheme ⋮ A combined approximating and interpolating ternary 4-point subdivision scheme ⋮ Six-point subdivision schemes with cubic precision ⋮ From approximating to interpolatory non-stationary subdivision schemes with the same generation properties ⋮ Creating a bridge between cardinal B\(r\)-spline fundamental functions for interpolation and subdivision ⋮ Reproduction of exponential polynomials by multivariate non-stationary subdivision schemes with a general dilation matrix ⋮ Interpolatory subdivision schemes with the optimal approximation order ⋮ An annihilator-based strategy for the automatic detection of exponential polynomial spaces in subdivision ⋮ A combined approximating and interpolating subdivision scheme with \(C^2\) continuity ⋮ Interpolating \(m\)-refinable functions with compact support: the second generation class ⋮ Nonstationary interpolatory subdivision schemes reproducing high-order exponential polynomials ⋮ A family of binary univariate nonstationary quasi-interpolatory subdivision reproducing exponential polynomials ⋮ A Novel Recursive Modification Framework for Enhancing Polynomial Reproduction Property of Interpolation Basis Functions

Cites Work

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• Extending cubic uniform B-splines by unified trigonometric and hyperbolic basis
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• An interpolating 4-point \(C^2\) ternary stationary subdivision scheme

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